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Undersampled Phase Retrieval with Outliers.

Daniel S Weller1, Ayelet Pnueli2, Gilad Divon2

  • 1Charles L. Brown Department of Electrical and Computer Engineering, University of Virginia, Charlottesville, VA 22904 USA.

IEEE Transactions on Computational Imaging
|January 16, 2016
PubMed
Summary
This summary is machine-generated.

This study introduces a robust phase retrieval framework for sparse image reconstruction from noisy, outlier-corrupted data. The method improves accuracy by combining majorization-minimization with robust data fitting, outperforming existing algorithms.

Keywords:
alternating direction method of multipliersmajorize-minimizephase retrievalsparsity

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Area of Science:

  • Image Reconstruction
  • Signal Processing
  • Computational Imaging

Background:

  • Phase retrieval is crucial for reconstructing images from undersampled magnitude data.
  • Existing methods struggle with data corrupted by noise and outliers.
  • Nonconvexity in phase retrieval poses significant algorithmic challenges.

Purpose of the Study:

  • To develop a general and robust framework for sparse image reconstruction.
  • To address challenges posed by outliers and noise in undersampled magnitude data.
  • To improve the accuracy and reliability of phase retrieval algorithms.

Main Methods:

  • A layered approach combining convex majorization-minimization with iterative ADMM optimization.
  • Incorporation of a robust 1-norm data fit term to handle outliers.
  • Utilizing multiple initial majorization vectors to navigate nonconvexity.

Main Results:

  • The proposed framework effectively reconstructs sparse images from corrupted data.
  • The robust data fit term significantly reduces reconstruction error in the presence of outliers and noise.
  • Demonstrated superior performance over competing algorithms in 1D and 2D simulations.

Conclusions:

  • The developed framework offers a general and robust solution for phase retrieval.
  • The integration of robust data fitting enhances resilience to data corruption.
  • This approach provides a significant advancement in sparse image reconstruction accuracy.